If you were to look at a .270 Winchester shooting a 130 grain bullet and a 7mm Mag shooting a 150, (Really, those are the two that compete against each other) there isn't much difference, honest. Lets look at it this way:
I just grabbed my Nosler #6 manual. I'm going to select a medium load from each cartridge. The .270 will send a 130 grain bullet at 3078 FPS. The 7mm will send a 150 at 3075 FPS. The highest .270 is 3158 and the highest 7mm is 3248. (Note I didn't say fastest because Colonal Craig uses that word, and I dispise his writing.

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Now, if you run those numbers through my Ballistics Program, I come up with the .270, zeroed at 200 yards will print:
100 1.4
200 0.0
300 -6.4
400 -18.8
500 -38.2
The 7mm will print:
100 1.4
200 0.0
300 -6.3
400 -18.3
500 -36.9
Will a deer or moose or antelope or elk tell the difference between these two? Probably not. Will you notice a difference between these two? On paper, not a chance. In recoil, well the 7mm uses 65 grains of powder, and the .270 only uses 55. So yeah, the 7mm will recoil more and have a louder blast. Will the 7mm do everything the .30-06 will but faster and better? I'm not sure how it will do that when it won't do anything a .270 will do better. Really will any animal you or I may hunt with a .270 or a .30-06 know the difference? Again, not a chance. Both cartridges when using good bullets are both capable of anything we could ever ask. I once traded a handgun for an FN Mauser in .270 with a 3X Weaver scope from an old fellow for my girlfriend. He used that rifle for everything, including grizzly bears. He still had all his skin to show for it too. The end result is you need to choose what rifle you like best, and don't worry about the cartridges. Either will treat you just fine.